Existence Results Of Positive Solutions Research Articles

Some properties and applications related to the ( 2 , p ) $(2,p)$ -Laplacian operator

In this paper, we give some properties about the $(2,p)$ -Laplacian operator ( $p>1$ , $p\ne2$ ), and consider the existence of solutions to two kinds of partial differential equations related to the $(2,p)$ -Laplacian operator by those properties. Specifically, we establish an existence result of positive solutions using fixed point index theory and an existence result of nodal solutions via the quantitative deformation lemma.

Positive Solutions of Singular Fractional Boundary Value Problem with p-Laplacian

In this paper, we present some new results concerning positive solutions for the singular fractional boundary value problem with p-Laplacian. By imposing some suitable conditions on the nonlinear term f, existence results of positive solutions are obtained. The proof is based upon theory of Leray–Schauder degree. The interesting point is the nonlinear term f(t, u) may be singular at \(u=0\).

Lichnerowicz-type equations on complete manifolds

Abstract Under appropriate spectral assumptions, we prove two existence results for positive solutions of Lichnerowicz-type equations on complete manifolds. We also give a priori bounds and a comparison result that immediately yields uniqueness for certain classes of solutions. No curvature assumptions are involved in our analysis.

Monotone iterative method for nonlinear fractional q-difference equations with integral boundary conditions

This paper investigates the existence of positive solutions for a class of nonlinear fractional q-difference equations with integral boundary conditions. By applying monotone iterative method and some inequalities associated with the Green’s function, the existence results of positive solutions and two iterative schemes approximating the solutions are established. An explicit example is given to illustrate the main result.

A note on the shooting method and its applications in the Stieltjes integral boundary value problems

In this paper, the existence results of positive solutions for three-point Riemann-Stieltjes integral BVPs (boundary value problems) is considered. By applying shooting method and comparison principle, we obtain some new results which extend the known ones. At the same time, the theorems in one of our published articles are corrected by another theorem in this paper.

Positive solutions of sub-superlinear Sturm–Liouville problems

In this paper, we introduce the notion of a strict lower/upper solution to nonlinear Sturm–Liouville boundary value problems. Based on the maximum principles, we establish a result of Leray–Schauder degree on the ordered intervals induced by the pairs of strict lower and upper solutions. Applying the result and the fixed point index theory in cones, we obtain the global existence results of positive solutions for sub-superlinear Sturm–Liouville problems.

An Existence Result of Positive Solutions for Fully Second-Order Boundary Value Problems

An existence result of positive solutions is obtained for the fully second-order boundary value problem -u′′(t)=f(t,u(t),u′(t)), t∈[0,1], u(0)=u(1)=0,wheref:[0,1]×R+×R→Ris continuous. The nonlinearityf(t,x,y)may be sign-changing and superlinear growth onxandy. Our discussion is based on the method of lower and upper solution.

Results for nonlinear fractional differential equations on pseudo-metric spaces with three boundary val

Abstract. In this paper, we investigate the existence of solutions in Gauge spaces for the nonlinear fractional differential equation boundary value problem With different boundary value and and different order 1 < a 2 and 0 < a < 1. where 0 < /31 < /32 < T and µ [O, T]and + is the standard Riemann-Lowville differentiation with f(t, u(t)) C([O, T] x [O, ), R). By using some fixed-point results on gauge spaces, some existence results of positive solutions are obtained.

Positive solutions for a class of higher-order singular semipositone fractional differential systems with coupled integral boundary conditions and parameters

Abstract In this paper, we study the existence of a class of higher-order singular semipositone fractional differential systems with coupled integral boundary conditions and parameters. By using the properties of the Green’s function and the Guo-Krasnosel’skii fixed point theorem, we obtain some existence results of positive solutions under some conditions concerning the nonlinear functions. The method of this paper is a unified method for establishing the existence of positive solutions for a large number of nonlinear differential equations with coupled boundary conditions. In the end, examples are given to demonstrate the validity of our main results. MSC:34B16, 34B18.

Existence of positive solution to boundary value problem of fractional differential equations with $$p$$ p -Laplacian operator

In this paper, we study the existence of positive solution to boundary value problem of fractional differential equations with $$p$$ -Laplacian operator. By using some fixed-point theorems on a convex cone, the new existence results of positive solution are obtained. In addition, an example is included to demonstrate the main result.

EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH m-POINT BOUNDARY VALUE CONDITIONS

In this paper,the Green's function for a class of fractional differential equations with m-point boundary value conditions is given and its properties are discussed.By using u_0-bounded operator and the fixed point index theory,some existence results of positive solutions for such multi-point boundary value problem are obtained,under some conditions concerning the first eigenvalue of the relevant linear operator.

Uniqueness of positive solutions for several classes of sum operator equations and applications

Abstract In this article we study several classes of sum operator equations on ordered Banach spaces and present some new existence and uniqueness results of positive solutions, which extend the existing corresponding results. Moreover, we establish some pleasant properties of nonlinear eigenvalue problems for several classes of sum operator equations. As applications, we utilize the main results obtained in this paper to study two classes nonlinear problems; one is the integral equation u ( t ) = λ ∫ a b G ( t , s ) f ( s , u ( s ) ) d s , where f and G are both nonnegative, λ &gt; 0 is a parameter; the other is the elliptic boundary value problem for the Lane-Emden-Fowler equation − Δ u = λ f ( x , u ) , u ( x ) &gt; 0 in Ω, u ( x ) = 0 on ∂ Ω, where Ω is a bounded domain with smooth boundary in R N ( N ≥ 1 ), λ &gt; 0 and f ( x , u ) is allowed to be singular on ∂ Ω. The new results on the existence and uniqueness of positive solutions for these problems are given, which complement the existing results of positive solutions for these problems in the literature. MSC:47H10, 47H07, 45G15, 35J60, 35J65.

Existence of Positive Solutions for a Nonlinear Higher-Order Multipoint Boundary Value Problem

We study the existence of positive solutions for a nonlinear higher-order multipoint boundary value problem. By applying a monotone iterative method, some existence results of positive solutions are obtained. The main result is illustrated with an example.

Existence result of positive solution for boundary value problems of fractional order with integro-differential boundary conditions

In this paper we study the following fractional boundary value problem with integro- differential boundary conditions ⎧ ⎪ ⎪ ⎩ D α+u(t) − f(t,u(t),D α−1 0+ u(t),D 1−α 0+ u(t)) = 0, t ∈ (0,T), n −1 α < n, u (j) (0 )= 0, D α−1 0+ u(T)+ � T

Existence of Positive Solutions for Nonlinear Third-Order Boundary Value Problem

We are concerned with the existence of positive solutions for the nonlinear third-order three-point boundary value problemu′′′(t)+λg(t)f(u(t))=0,0&lt;t&lt;1,u(0)=αu(η),u′(0)=u′′(1)=0, where0&lt;η&lt;1,0&lt;α&lt;1,λis a positive parameter,g:(0,1)→[0,∞), and f:[0,∞)→[0,∞)is continuous. We construct Green’s function for the associated linear boundary value problem and obtain some useful properties of Green’s function. Finally, by using fixed-point index theorem in cones, we establish the existence results of positive solutions for the boundary value problem an example illustrates the application of the results obtained.

Monotone Iterative Methods of Positive Solutions for Fractional Differential Equations Involving Derivatives

This paper studies the existence and computing method of positive solutions for a class of nonlinear fractional differential equations involving derivatives with two-point boundary conditions. By applying monotone iterative methods, the existence results of positive solutions and two iterative schemes approximating the solutions are established. The interesting point of our method is that the iterative scheme starts off with a known simple function or the zero function and the nonlinear term in the fractional differential equation is allowed to depend on the unknown function together with derivative terms. Two explicit numerical examples are given to illustrate the results.

Some Existence Results of Positive Solution to Second-Order Boundary Value Problems

We study the existence of positive and monotone solution to the boundary value problemu′′(t)+f(t,u(t))=0,0⩽t⩽1,u(0)=ξu(1),u'(1)=ηu'(0), whereξ,η∈(0,1)∪(1,∞). The main tool is the fixed point theorem of cone expansion and compression of functional type by Avery, Henderson, and O’Regan. Finally, four examples are provided to demonstrate the availability of our main results.

Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter

In this paper, we study the existence of positive solutions for the following nonlinear fractional differential equations with integral boundary conditions:D0+αu(t)+h(t)f(t,u(t))=0,0<t<1,u(0)=u′(0)=u″(0)=0,u(1)=λ∫0ηu(s)ds,where 3<α≤4,0<η≤1,0⩽ληαα<1,D0+α is the standard Riemann–Liouville derivative. h(t) is allowed to be singular at t=0 and t=1. By using the properties of the Green function, u0-bounded function and the fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator, we obtain some existence results of positive solution.

A new existence result of positive solutions for the Sturm–Liouville boundary value problems

We prove a new existence result of positive solutions for the Sturm–Liouville problems. Different from the existing research, we do not assume that a nonlinearity term f has numerical and functional lower bounds or satisfies some usual limit conditions.

An Existence Theorem for Semi-linear Elliptic Systems

Abstract We study the following boundary value problem of semi-linear elliptic systems Δu + f(x, u, ∇u) =0 in Ω, u =0 on ∂Ω where Ω ⊂ ℝn (n ≥ 2) is a connected and bounded smooth domain, and u and f are real vector-valued functions. Under appropriate conditions on the function f, we establish a general existence result for positive solutions. We continue our earlier works [15, 16, 17] and, in particular, remove a requirement of the cooperative structure on elliptic systems. As examples, we consider the stationary Klein-Gordon-Maxwell system and Maxwell- Schrodinger system, both lacking the cooperative structure..